Barack Obama's campaign team ratcheted up the rhetoric in the White House election battle on Thursday, claiming the Republican contender Mitt Romney may have committed a crime over how he portrayed his involvement with Bain Capital, the company where he made his fortune.

In remarks that took the campaign to a new, uglier phase, Obama's deputy campaign manager Stephanie Cutter said Romney had either misrepresented his position to government regulators or had lied to the American people.

Romney has been claiming for a decade that he ceded control of Bain Capital in 1999 to run the 2002 Salt Lake City Winter Olympics, but Bain filings to the Securities and Exchange Commission (SEC) list him three years later as the "sole stockholder, chairman of the board, chief executive officer and president".

The issue is significant because the Obama campaign claims that after 1999, Bain Capital, an investment vehicle, was involved in lay-offs, bankruptcies and the outsourcing of American jobs to China, Mexico and elsewhere. The remarks are a potent charge in a tight election – Obama and Romney are neck-and-neck in the polls – in which unemployment is the main issue.

Following a report in the Boston Globe that identified the SEC filings, Cutter called on Romney to "come clean" about his role in Bain.

She said that there were two ways to interpret the story: either Romney was "misrepresenting his position at Bain" to the Securities and Exchange Commission "which is a felony" or he is "misrepresenting his position at Bain to the American people. If that's the case, if he was lying to the American people, that's a real character and trust issue."

Responding to the Globe report, Romney press secretary Andrea Saul said in a statement: "The article is not accurate. As Bain Capital has said, as governor Romney has said, and as has been confirmed by independent fact checkers multiple times, governor Romney left Bain Capital in February of 1999 to run the Olympics and had no input on investments or management of companies after that point."

Matt Rhoade, Romney's campaign manager, called on Obama to apologise. "President Obama's campaign hit a new low today when one of its senior advisers made a reckless and unsubstantiated charge to reporters about Mitt Romney that was so over the top that it calls into question the integrity of their entire campaign," Rhoades said.

"President Obama ought to apologise for the out-of-control behavior of his staff, which demeans the office he holds. Campaigns are supposed to be hard fought, but statements like those made by Stephanie Cutter belittle the process and the candidate on whose behalf she works."

The issue has dogged Romney since the Republican primaries earlier this year when opponents such as former House speaker Newt Gingrich and Texas governor Rick Perry hammered him for presiding over the closure of firms. Perry accused him of "vulture capitalism".

The Obama campaign team has come at him much harder, seeking to portray him as rich, secretive and out of touch with ordinary Americans. As well as his record at Bain Capital, they are running a separate campaign calling on him to publish his tax returns, particularly after Vanity Fair last week reported he had accounts in Switzerland, the Cayman Islands, Bermuda and other tax havens.

Romney has never denied that he remained the sole owner of Bain Capital until 2002 but he insisted he gave up control of the company in 1999 to help organise the Winter Olympics in Salt Lake City in 2002 and never went back, focusing instead full-time on his political career, successfully campaigning in 2002 to become governor of Massachusetts.

But new documents complicate the issue. SEC filings from Bain Capital after 1999 repeatedly show him listed as the firm's sole stockholder, chairman of the board, chief executive officer and president.

While this is far from proof that Romney was involved in the day-to-day running of the company, engaged in making strategic decisions or meeting people on behalf of the firm, the Obama campaign says the onus is him to prove otherwise. Obama officials called on Romney to ask Bain to release the minutes of its meetings for 1999 to 2002.

Bob Bauer, a lawyer with the Obama campaign, echoing Cutter's point that the SEC filings are a "serious business", hinted that there would be more to come about Romney's involvement with Bain. He told reporters to stay tuned.

The nastiness of the campaign so early on, with more than three months of electioneering still to go, reflects a race that that may be decided by narrow margins, possibly America's dismal jobs figures, an issue the Democrats are attempting to deflect attention from, or by a perception of Romney as an exceedingly rich man.

An Obama campaign ad released on Thursday and aimed at Latinos was naked in potraying Romney an unsympathetic, wealthy figure who did not care about ordinary Americans.

Romney was in Wyoming on Thursday for a fundraiser at the home of former vice-president Dick Cheney. Although Romney is neck-and-neck with Obama in the polls, he is outstripping him in terms of fundraising, having taken in $106m in June compared with Obama's $71m.

A Rasmussen poll Thursday put Romney on 46% to Obama's 45%, while Gallup the previous day had Romney on 45% and Obama on 47%.